The roots of the quadratic equation $\sqrt{3}x^{2}+10x+7\sqrt{3}=0$ are
- $\left [ -\sqrt{3},-\frac{7}{\sqrt{3}} \right ]$
- $\left [ \frac{1}{\sqrt{3}},\frac{\sqrt{3}}{7} \right ]$
- $\left [ \sqrt{3},\frac{7}{\sqrt{3}} \right ]$
- $\left [ \sqrt{3},-\frac{7}{\sqrt{3}} \right ]$
Reveal answer
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A
Correct answer
Explanation
The quadratic equation can be factored by splitting the middle term: sqrt(3)x^2 + 3x + 7x + 7*sqrt(3) = 0, which simplifies to (x + sqrt(3))(sqrt(3)*x + 7) = 0. Solving for x gives the roots as -sqrt(3) and -7/sqrt(3).
AI explanation
To solve sqrt(3)x^2 + 10x + 7*sqrt(3) = 0, we can split the middle term. We rewrite the equation as sqrt(3)x^2 + 3x + 7x + 7*sqrt(3) = 0. Factoring by grouping gives sqrt(3)x(x + sqrt(3)) + 7(x + sqrt(3)) = 0. This yields the factored form (sqrt(3)x + 7)(x + sqrt(3)) = 0. Equating each factor to zero gives the roots as -7/sqrt(3) and -sqrt(3).